Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in PYTHON3):

Solution:
import math
n, h = [float(x) for x in input().split()]
base=1
ctgL= (base/2)/h

expectedArea = (1*h/2)/n
expectedArea=expectedArea/2

new_base = base/2
curr_height = h

def bin_search(new_base, min_height, max_height):
    try_height = (min_height+max_height)/2
    area = ((2*new_base - try_height*ctgL)/2)*try_height
    if(abs(area-expectedArea)<1e-9):
        return try_height
    else:
        if area>expectedArea:
            return bin_search(new_base, min_height,try_height)
        else:
            return bin_search(new_base, try_height, max_height)
def calculate_new_base(old_base, height):
    return old_base-height*ctgL
cuts = []
for i in range(int(n)-1):
    cut_height = bin_search(new_base, 0, curr_height)
    # print(cut_height)
    cuts.append(cut_height)
    new_base = calculate_new_base(new_base,cut_height)
    curr_height = curr_height - cut_height
    # print(new_base, curr_height)
cuts_sum=0
to_print = []
for cut in cuts:
    cuts_sum+=cut
    to_print.append((h-cuts_sum))
for x in reversed(to_print):
    print(x, end=" ")